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3 years ago

Is x^5 - 5x^4 + 4x^3 - 3x^2 + 2x + 1 a polynomial

Mathematics

1 answer:

vfiekz [6]3 years ago

4 0

Answer:

yes

Step-by-step explanation:

Polynomial Long Division :

4.3 Polynomial Long Division

Dividing : x5-5x4+10x3-10x2+5x-1

("Dividend")

By : x-1 ("Divisor")

dividend x5 - 5x4 + 10x3 - 10x2 + 5x - 1

- divisor * x4 x5 - x4

remainder - 4x4 + 10x3 - 10x2 + 5x - 1

- divisor * -4x3 - 4x4 + 4x3

remainder 6x3 - 10x2 + 5x - 1

- divisor * 6x2 6x3 - 6x2

remainder - 4x2 + 5x - 1

- divisor * -4x1 - 4x2 + 4x

remainder x - 1

- divisor * x0 x - 1

remainder 0

Quotient : x4-4x3+6x2-4x+1 Remainder: 0

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ABCDEFGHIJ is a regular decagon with a radius of 25.89 units and a side length of 16. Find the area of ABCDEFGHIJ. Round the ans

slamgirl [31]

A decagon is a polygon which has ten sides. A regular decagon is characterized by equal side lengths. An important dimension of this polygon is the side length. The area is expressed as:
A=(5/2)a^2(√5+(2√5))
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4 years ago

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Which equation has a constant of proportionality equal to 555? Choose 1 answer:

zysi [14]

Answer:

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Step-by-step explanation:

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The indicated function y1(x) is a solution of the given differential equation. use reduction of order or formula (5) in section

Ber [7]

Given that $y_1=e^{2x/3}$ , we can use reduction of order to find a solution $y_2=v(x)y_1=ve^{2x/3}$ .

$\implies {y_2}'=\dfrac23ve^{2x/3}+v'e^{2x/3}=\left(\dfrac23v+v'\right)e^{2x/3}$
$\implies{y_2}''=\dfrac23\left(\dfrac23v+v'\right)e^{2x/3}+v''e^{2x/3}=\left(\dfrac49v+v'+v''\right)e^{2x/3}$

$\implies9y''-12y'+4y=0$
$\implies 9\left(\dfrac49v+v'+v''\right)e^{2x/3}-12\left(\dfrac23v+v'\right)e^{2x/3}+4ve^{2x/3}=0$
$\implies9v''-3v'=0$

Let $u=v'$ , so that

$9u'-3u=0\implies 3u'-u=0\implies u'-\dfrac13u=0$
$e^{-x/3}u'-\dfrac13e^{-x/3}u=0$
$\left(e^{-x/3}u\right)'=0$
$e^{-x/3}u=C_1$
$u=C_1e^{x/3}$

$\implies v'=C_1e^{x/3}$
$\implies v=3C_1e^{x/3}+C_2$

$\implies y_2=\left(3C_1e^{x/3}+C_2\right)e^{2x/3}$
$\implies y_2=3C_1e^x+C_2e^{2x/3}$

Since $y_1$ already accounts for the $e^{2x/3}$ term, we end up with

$y_2=e^x$

as the remaining fundamental solution to the ODE.

7 0

3 years ago

What number is one hundred thousand more than 75,000?

Gwar [14]

The answer is 175,000

6 0

3 years ago

Please help with clear explanation

Arlecino [84]

Answer:

102

Step-by-step explanation:

You can split that shape up into 2 rectangles to make it easier get the area of each rectangle and add them together.

Step 1

Identify the width and height

Step 2

Multiply the sides to get the answer

For example if we split the shape we will have 9,10 and 2,6

9 times 10 is 90

and 2 times 6 is 12

Add the 2 and get 102

Hopefully this helped.

8 0

4 years ago